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. 2024 Jul 3;64(14):5671–5679. doi: 10.1021/acs.jcim.4c00764

Ligand Binding Affinity Prediction for Membrane Proteins with Alchemical Free Energy Calculation Methods

Han Zhang 1, Wonpil Im 1,*
PMCID: PMC11267607  PMID: 38959405

Abstract

graphic file with name ci4c00764_0006.jpg

Alchemical relative binding free energy (ΔΔG) calculations have shown high accuracy in predicting ligand binding affinity and have been used as important tools in computer-aided drug discovery and design. However, there has been limited research on the application of ΔΔG methods to membrane proteins despite the fact that these proteins represent a significant proportion of drug targets, play crucial roles in biological processes, and are implicated in numerous diseases. In this study, to predict the binding affinity of ligands to G protein-coupled receptors (GPCRs), we employed two ΔΔG calculation methods: thermodynamic integration (TI) with AMBER and the alchemical transfer method (AToM) with OpenMM. We calculated ΔΔG values for 53 transformations involving four class A GPCRs and evaluated the performance of AMBER-TI and AToM-OpenMM. In addition, we conducted tests using different numbers of windows and varying simulation times to achieve reliable ΔΔG results and to optimize resource utilization. Overall, both AMBER-TI and AToM-OpenMM show good agreement with the experimental data. Our results validate the applicability of AMBER-TI and AToM-OpenMM for optimization of lead compounds targeting membrane proteins.

Introduction

The advantages of predicting relative ligand binding affinity (ΔΔG) using alchemical binding free energy methods include cost-effectiveness, speed, enhanced understanding of binding mechanisms, and optimization of lead compounds. Free energy perturbation (FEP) and thermodynamic integration (TI) are the most popular choices for ΔΔG calculations due to their robust theoretical foundations1−4 together with improved force field quality.5−7 In addition, a recently developed method, alchemical transfer method (AToM),8,9 has demonstrated excellent agreement with experimental results, further enriching the repertoire of reliable computational tools in this field. Unlike other alchemical methods that achieve the transformation from one molecule to another through parameter interpolation approaches (i.e., scaling parameters of the potential energy function to smoothly convert one ligand into another via an alchemical transformation), AToM utilizes coordinate transformations to map the potential energy functions of the unbound and bound states. The AToM is freely available as an open-source plugin for OpenMM10 (AToM-OpenMM).

Numerous studies have demonstrated high accuracy of alchemical methods for predicting ΔΔG, particularly in soluble proteins.11−16 However, there remains a paucity of studies focusing on ΔΔG calculations for membrane proteins. Indeed, compared to the soluble protein targets, the application of ΔΔG calculations in membrane proteins is more challenging because of the increased complexity of system setup, the presence of buried water molecules, and the intricacies in lipid composition. In addition, although the reliability of AToM-OpenMM for ligand binding affinity calculations in soluble proteins has been shown, its extensive application to membrane proteins has yet to be explored. A recent review paper discusses the current state of research in alchemical free energy calculations for membrane proteins.17

The critical role of membrane proteins in modulating cellular activities and signaling underscores their importance as crucial drug targets. Understanding ligand binding affinities is essential for the rational design of effective drugs targeting these vital components of cellular processes. Membrane proteins, like G protein-coupled receptors (GPCRs)18 and ion channels, possess specific binding sites where drug-like small molecules can effectively interact with them. GPCRs, essential for signal transduction, are prominent membrane proteins targeted by numerous drugs, thereby garnering significant attention from researchers for the application of ΔΔG calculations on GPCRs. In 2016, for example, Lenselink et al. applied FEP+12 for ΔΔG prediction against four GPCRs: adenosine A2A,19 β1-adrenergic,20 δ-opioid,21 and chemokine CXCR4.22,23 Their study demonstrated a great agreement between predicted values and experimental results, featuring a high-ranking correlation (average Spearman coefficient ρ = 0.55) and a low root-mean-square error (RMSE) of 0.80 kcal/mol. This level of accuracy is comparable to that achieved with soluble proteins using alchemical methods. As another example, a mechanosensitive ion channel PIEZO124 emerges as a critical membrane protein, as PIEZO1 plays a crucial role in transducing mechanical forces into cellular signals, which is pivotal in many important physiological processes in vertebrate organisms.25 In addition to responding to mechanical stimuli, PIEZO1 can be activated by small molecules like Yoda1.26 Therefore, understanding the interactions between PIEZO1 and its activators holds promise for clinical benefits and contributes to drug optimization efforts. In 2023, Jiang et al. utilized FEP coupled with replica-exchange MD (FEP/REMD) implemented in NAMD27 and TI implemented in AMBER (AMBER-TI)28 for the absolute binding free energy (ΔG) and ΔΔG calculations for Yoda1 and seven analogs.29 Their study showed excellent agreement among different alchemical methods and with experimental results. However, it is worth noting that although they utilized AMBER-TI for the ΔΔG predictions in PIEZO1, the scope of calculations was relatively limited with only seven transformations included.

In this study, we have applied AMBER-TI for 53 pairs across four different GPCRs, demonstrating the extensive applicability of AMBER-TI for ΔΔG predictions in membrane proteins. In addition, we employed AToM-OpenMM ΔΔG calculations for the same 53 transformations to investigate its potential and reliability in membrane proteins. Furthermore, we investigated the impacts of excluding the membrane bilayer from the system on ΔΔG predictions.

Methods

Conventional Molecular Dynamics Simulations

The all-atom simulation systems were prepared with CHARMM-GUI Membrane Builder(30) for four GPCR structures with the following PDB IDs: 3PWH (adenosine A2A),31 3ZPQ (β1-adrenergic),20 4N6H (δ-opioid),32 and 3ODU (chemokine CXCR4).33 Each protein was embedded in a pure POPC bilayer solvated by 0.15 M KCl or NaCl with a TIP3P water model.34 The water molecules and ions present in the PDB files were retained during the system generation. The following force fields were used for the MD simulations: ff19SB6 for protein, generalized Amber force field (GAFF) 27 for ligand, and Lipid2135 for lipid. Equilibration of the simulation systems followed the standard procedure outlined by CHARMM-GUI.36,37 Pressure was regulated by a semi-isotropic Monte Carlo barostat with a pressure relaxation time of 1.0 ps for equilibration steps with the NPT (constant particle number, pressure, and temperature) ensemble. The particle mesh Ewald (PME) method38,39 was employed to handle the long-range electrostatic interactions, and a cutoff of 9 Å was used for nonbonded interactions. The simulations were conducted utilizing hydrogen mass repartitioning (HMR) with a 4 fs time step.40,41 All production MD simulations were performed for 100 ns in the NPT ensemble at 300 K and 1 atm using AMBER20 pmemd.cuda.42 The equilibrated snapshot of each complex structure served as the initial point for preparing AMBER-TI and AToM-OpenMM systems. The ligand coordinates in each equilibrated structure were used as the initial binding mode. For each system, the core structure of the ligand was kept at its original coordinates, and the R groups were prepared using Avogadro.43

AMBER-TI

To systematically and efficiently conduct large-scale ΔΔG calculations, we carefully selected at least 10 transformations from each protein system (based on the Lenselink data set23 in Figures S1 to S4). These transformations were chosen to ensure that the experimental ΔΔG values cover a relatively large range. Antechamber and parmchk2 were used to parametrize the ligands, and their charges were calculated using AM1-BCC44 for GAFF2. LEaP was used to generate a topology file (parm7) and coordinate file (rst7). In the end, ParmEd45 was used to apply HMR to the system.

Each transformation pair system was generated with a unified protocol in which both electrostatic and van der Waals (vdW) interactions are simultaneously scaled by the softcore potentials.11,42 ΔΔG prediction between two ligands is calculated as follows:

graphic file with name ci4c00764_m001.jpg 1

where ΔGA→Bcmpx and ΔGA→Bsolv represent the alchemical transformations of ligand A to ligand B in the complex and solvent, respectively (Figure 1A). The ΔG values can be calculated by ∫10⟨∂U(λ)/∂λ, where U(λ) is the λ coupled potential energy and λ is a coupling parameter ranging from 0 to 1. The integration is calculated by averaging ∂U(λ)/∂λ at each intermediate λ state. Twelve λ windows (0.0, 0.0479, 0.1151, 0.2063, 0.3161, 0.4374, 0.5626, 0.6839, 0.7937, 0.8850, 0.9521, and 1.0) were employed for each complex and solution system. The ΔG values were obtained by summing of numerical integration over the quadrature points of ∂U/∂λ with associated weights. Long-range electrostatics were treated with the PME method,38,39 and the vdW interactions were computed with a cutoff distance of 9 Å. The second-order smoothstep softcore potential, SSC(2), was applied in the simulation with parameter values set to 0.2 for α and 50 Å2 for β.42 Equilibration was conducted for 5 ps employing the NPT ensemble after minimization in each λ window. AMBER-TI simulations were performed in the NPT ensemble at 300 K and 1 atm by employing the pmemd.cuda module of AMBER20. Pressure was regulated by an isotropic MC barostat with a pressure relaxation time of 2.0 ps. All alchemical transformations were executed with a 4 fs time step using HMR. For statistical analysis, four independent runs were performed for each pair, and the mean value was recorded as ΔΔG for all calculations throughout this work.

Figure 1.

Figure 1

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Free energy diagram for (A) AMBER-TI and (B) AToM-OpenMM. The protein is represented in purple, the membrane bilayer in green, the aqueous solvent in blue, the initial ligand in red, and the final ligand in yellow. For AToM-OpenMM, the λ values for both legs end at 1/2, indicating that 50% of ligands A and B are present in both the binding site and the solvent bulk [R(AB)1/2 + (BA)1/2].

AToM-OpenMM

ΔΔG calculations were also performed with AToM-OpenMM for the same 53 transformations using identical initial structures. The force fields employed in AToM-OpenMM were the same as those used in AMBER-TI, and the LEaP program was used for system setup. As shown in Figure 1B, the AToM-OpenMM ΔΔG calculation consists of two independent legs: Leg 1 and Leg 2. In Leg 1, the λ parameter begins at 0, where ligand A is bound to the binding site of the receptor R and ligand B is in the solvent bulk (state RA + B); λ ends at 1/2, which denotes the alchemical intermediate state, where 50% of ligands A and B are present in both the binding site and solvent bulk. In Leg 2, the calculation starts with ligand B bound to the binding site and ligand A in the solvent bulk (state RB + A) and similarly ends at 1/2. ΔΔG is the difference in free energy change between Leg 1 and Leg 2.

The alchemical potential energy function is defined as

graphic file with name ci4c00764_m002.jpg 2

where λ ranges from 0 to 1/2 and x represents the atomic coordinates of the system, including the receptor, ligand A, ligand B, solvent, and membrane lipid. URA + B(x) represents the potential energy of the system before the application of the coordinate displacement. u(x) is the perturbation energy, which is defined as

graphic file with name ci4c00764_m003.jpg 3

and Wλ(u) is the generalized softplus alchemical perturbation function:

graphic file with name ci4c00764_m004.jpg 4

As described in detail by Pal et al.46 and Khuttan et al.,47 the parameters λ1, λ2, α, and u0 are functions of λ. To prevent singularities near the initial state of the alchemical transformation, the soft-core perturbation energy function is designed as

graphic file with name ci4c00764_m005.jpg 5

where

graphic file with name ci4c00764_m006.jpg 6

In this study, according to the original AToM studies,9,46,47 the parameters umax, uc, and α are set to 200 kcal/mol, 100 kcal/mol, and 1/16, respectively.

In this work, for each leg, two sets of λ windows were tested: one with 6 evenly spaced λ-states from 0 to 1/2 and the other with 11 evenly spaced λ-states covering the same range. The detailed parameters of λ1, λ2, α, and u0 are listed in Tables S1 and S2. After energy minimization, thermalization, and relaxation, following the standard procedure of AToM-OpenMM, we conducted asynchronous Hamiltonian replica exchange MD conformational sampling. Long-range electrostatics were handled using PME method,38,39 and the vdW interactions were calculated with a cutoff distance of 9 Å. The simulations were performed using a 4 fs time step with HMR, maintaining constant volume and temperature (300 K) with the Langevin thermostat. Four independent runs were conducted for each transformation pair to derive a mean ΔΔG value.

Free Energy Calculation without Membrane

In a membrane protein simulation system, the presence of the membrane often leads to a larger system size and a higher number of atoms. As a result, computing one ΔΔG value requires more resources and time than those in a solution system. Thus, we built AMBER-TI systems in solution for the same 53 pairs by using initial structures from the PDBs. This allows us to assess whether similar accuracy in ΔΔG prediction can be achieved in the absence of the membrane compared with simulations containing a membrane. The same protocol used in the membrane-present system was applied for the AMBER-TI calculations without a membrane.

Results and Discussion

Performance of ΔΔG Prediction

No matter whether AMBER-TI or AToM-OpenMM is used, obtaining an ΔΔG value requires computing the ΔG value for each leg in Figure 1. Previously, for AMBER-TI, we determined that 12 λ windows are sufficient to obtain reliable results.48 Therefore, we chose to use 12 λ windows for AMBER-TI calculations while testing 6 and 11 windows for each ΔG calculation in AToM-OpenMM. The scatter plots in Figure 2 compare the ΔΔG prediction of AMBER-TI and AToM-OpenMM with the experimental data. The figure also provides the overall mean unsigned error (MUE), root-mean-square error (RMSE), Matthew’s correlation coefficient (MCC),49 Pearson’s correlation (r), and Spearman’s rank correlations (ρ) for the 53 transformations across four protein targets.

Figure 2.

Figure 2

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Correlation between the predicted and experimental ΔΔG values of ligands across four different GPCRs. The results from AMBER-TI and AToM-OpenMM are depicted in cool (blue and cyan) and warm colors (red, yellow, and violet), respectively. The error bars are the standard errors of four independent AMBER-TI or AToM-OpenMM runs. The dashed 1:1 line indicates the perfect agreement. The dark- and light-shaded gray areas represent predictions within 1 and 2 kcal/mol from the experiment values, respectively. The figure also summarizes the overall MUE, RMSE, MCC, r, and ρ for the 53 pairs.

According to the resulting statistics, AMBER-TI demonstrates a high level of accuracy in predicting ΔΔG using 12 λ windows (ranging from 0 to 1) for both complex and solution systems. Conducting 5 ns simulations for each window yielded metrics of an MUE of 0.83, RMSE of 1.09, MCC of 0.52, r of 0.77, and ρ of 0.76. Extending the simulation length to 10 ns per window also results in a similar level of accuracy in terms of MUE, RMSE, MCC, r, and ρ.

For AToM-OpenMM, we tested two sets of λ windows, either 6 or 11 (ranging from 0 to 1/2), for each leg. Both sets demonstrated comparable accuracy. In addition, we extended the simulations to 10 ns for the 6 λ windows set, which also resulted in similar accuracy levels across the metrics. Our benchmark tests using AToM-OpenMM suggest that 6 λ windows (from 0 to 1/2) and 5 ns per window are sufficient for obtaining reliable ΔΔG values.

When the two methods are compared with experimental data, AMBER-TI slightly outperforms AToM-OpenMM in terms of ranking correlations, with r of 0.77 compared to 0.70 and with ρ of 0.76 compared to 0.66. The detailed MUE, RMSE, MCC, r, and ρ of each GPCR are listed in Tables S3–S6. To assess the robustness of these metrics, the 95% confidence intervals of MUE, RMSE, r, and ρ were obtained using bootstrapping by resampling ΔΔG values 5000 times with replacement. Across individual protein systems, the performance of AMBER-TI and AToM-OpenMM shows comparable accuracy. Specifically, AMBER-TI demonstrates slightly better ΔΔG prediction in δ-opioid and chemokine CXCR4 systems, whereas AToM-OpenMM performs better prediction for β1-adrenergic. Both methods exhibit similar performances for adenosine A2A. Therefore, our results suggest that both AMBER-TI and AToM-OpenMM are reliable for estimating the binding affinity of the ligands in the membrane proteins.

We further compared the results within two alchemical binding free energy methods. As shown in Figure 3, the predicted results from AMBER-TI and AToM-OpenMM exhibit excellent agreement with an overall r of 0.94, ρ of 0.89, MUE of 0.43, RMSE of 0.58, and MCC of 0.78. This indicates that two different alchemical approaches yield highly consistent predictions, enhancing the confidence in their reliability and applicability. However, for individual system cases, there may be slight differences in consistency. For example, adenosine A2A shows the best agreement between two methods, whereas δ-opioid exhibits the worst. This difference might be attributed to the larger transformations involved in the pairs in the δ-opioid system, as handling large transformation is one of the significant challenges in ΔΔG calculations.

Figure 3.

Figure 3

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Comparison between predicted ΔΔG values from AMBER-TI and AToM-OpenMM. Results from adenosine A2A, β1-adrenergic, δ-opioid, and chemokine CXCR4 systems are colored red, blue, cyan, and yellow, respectively. The error bars are the standard errors of four independent AMBER-TI or AToM-OpenMM runs. The figure summarizes the overall MUE, RMSE, MCC, r, and ρ for the 53 pairs and individual metrics for four GPCRs.

We then compared our results with those obtained by Lenselink et al. Although our results overall align well with the experimental data and show consistency between our two alchemical binding free energy calculation methods, there are some divergences for certain pairs when compared to the work of Lenselink et al. For instance, in the δ-opioid receptor, for the transformation pair from L10 to L16, we obtained ΔΔG values of 0.32 ± 0.29 and 0.96 ± 0.63 kcal/mol from AMBER-TI and AToM-OpenMM, respectively. In contrast, Lenselink et al. reported a value of −2.40 ± 0.13 kcal/mol (based on the reverse transformation result from L16 to L10) using FEP+, which shows better agreement with the experimental data (−2.46 kcal/mol). However, for the transformation from L11 to L12, our results from AMBER-TI (−0.86 ± 0.37 kcal/mol) and AToM-OpenMM (0.09 ± 0.51 kcal/mol) align better with the experimental value (−0.77 kcal/mol), whereas Lenselink et al. obtained 0.46 ± 0.09 kcal/mol. We observed similar patterns in the chemokine CXCR4 system. For the transformation pair from 1d to 1c, the ΔΔG value from the FEP+ calculation (−0.49 ± 0.15 kcal/mol) of Lenselink et al. shows better agreement with the experimental data (−0.57 kcal/mol) compared to our results from AMBER-TI (−4.13 ± 0.19 kcal/mol) and AToM-OpenMM (−4.17 ± 0.62 kcal/mol). However, for the pair from 1d to 1t, AMBER-TI and AToM-OpenMM provide better results with −3.99 ± 0.06 and −3.36 ± 0.78 kcal/mol, respectively, whereas FEP+ shows relatively worse results with −0.04 ± 0.22 kcal/mol compared to the experimental result of −4.22 kcal/mol. Interestingly, the results from AMBER-TI and AToM-OpenMM exhibit a high degree of consistency irrespective of their predictive accuracy. Therefore, we identified two possible reasons why our results are not aligning with those obtained using FEP+ by Lenselink et al.: the differences in the force field selection and initial binding poses. We utilized the AMBER force field for both AMBER-TI and AToM-OpenMM, whereas Lenselink et al. used the OPLS2.1 and OPLS3 force fields for FEP+. In addition, we generated alchemical binding free energy systems using the snapshots obtained from conventional MD simulations of 100 ns, which included the ligand coordinates. In contrast, Lenselink et al. generated systems directly using the crystal structure coordinates or after employing core-constrained docking and short simulations.

Convergence

For each transformation pair, we obtained the ΔΔG value from four independent runs. In each independent run, the initial 1 ns simulation was discarded from the analysis. Convergence plots of an example, the transformation pair of L12 to L18 in the δ-opioid receptor, are shown in Figure 4. The time evolution of the AMBER-TI and AToM-OpenMM results suggests that a plateau is reached during the simulations (Figure 4B). The difference in ΔΔG calculation between 5 and 10 ns/window is negligible, with a variation of only 0.14 kcal/mol.

Figure 4.

Figure 4

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(A) The ligand structures of a transformation pair from L12 to L18 in the δ-opioid receptor are displayed along with the predicted ΔΔG values from both AMBER-TI and AToM-OpenMM, as well as experimental data. (B) The time evolution of the AMBER-TI and AToM-OpenMM results is illustrated by using accumulated simulation data, demonstrating convergence of the ΔΔG values. (C, D) The distribution of perturbation energy for the alchemical states with λ ranging from 0 to 1/2 using either 6 λ or 12 λ windows. Both figures show good overlaps between neighboring distributions. The color gradient indicates λ values, transitioning from red (0) to violet (1/2), following the rainbow color scheme.

For AToM-OpenMM, all published studies have utilized 11 λ windows for each leg.8,9,50 To further assess the convergence using 6 λ windows for each leg, we analyzed the perturbation energy distributions for the alchemical states. Figure 4C shows a substantial overlap between adjacent distributions, suggesting that using 6 λ windows for each leg yields converged results in our benchmark tests.

Performance of ΔΔG Prediction in Membrane-Absent Conditions

The overall performance of ΔΔG prediction for both membrane-present and membrane-absent systems using AMBER-TI is summarized in Figure 5, along with the MUE, RMSE, MCC, r, and ρ values for the same 53 pairs. To examine the influence of the AMBER-TI simulation time, we extended the simulations to 20 ns per window for both membrane-present and membrane-absent systems. ΔΔG results were calculated at every 5 ns interval (e.g., 5, 10, 15, and 20 ns) for the extended simulations. According to the calculated MUE, RMSE, MCC, r, and ρ values, the performance in both membrane-present and membrane-absent systems remains consistent with their respective 5 ns simulations. This further suggests that a 5 ns simulation per window is sufficient for obtaining reliable ΔΔG values in our benchmark tests.

Figure 5.

Figure 5

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Correlation between predicted and experimental ΔΔG values of ligands across four different GPCRs in the membrane-present (cool colors: blue, cyan, and green) and membrane-absent (warm colors: red, orange, and yellow) systems. The error bars are the standard errors of four independent AMBER-TI runs. The dashed 1:1 line indicates the perfect agreement. The dark- and light-shaded gray areas represent predictions within 1 and 2 kcal/mol from the experiment values, respectively. The figure also presents the overall MUE, RMSE, MCC, r, and ρ for the 53 pairs.

Overall, the performance is better when the system includes a membrane. For example, with each λ conducted over a 5 ns simulation, the lower MUE (0.83 compared to 1.15) and RMSE (1.09 vs 1.40) and the higher MCC (0.52 vs 0.32) indicate that ΔΔG calculations more closely align with experimental results when a membrane is present. In addition, the higher r (0.77 vs 0.67) and ρ (0.76 vs 0.62) values suggest better ranking correlations in membrane-present conditions.

In a membrane protein system, the presence of membrane provides a hydrophobic environment that stabilizes the transmembrane domains (TMDs) and helps maintain the protein’s structures during the simulations. We measured the root-mean-square deviation (RMSD) of the protein’s TMDs to assess whether the protein’s conformation also remains stable in the membrane-absent systems (Figure S5). Notably, the membrane-absent systems show larger RMSD values, indicating reduced protein structural stability compared with that in the membrane-present system. The time evolution of RMSD for the example cases demonstrates how RMSD values change during the 20 ns simulations (Figure S6). Clearly, without the membrane, the protein structures are more variable and deviate from the initial structures.

Next, we calculated the RMSD of the common core region of two ligands after aligning TMDs of the protein to determine if the ligands remain bound to the binding site during AMBER-TI simulations. As shown in Figure S7, the ligands in chemokine CXCR4 system show higher RMSD values without the membrane. However, as shown in Figure 5D and Table S6, the accuracy of ΔΔG predictions is similar for both membrane-present and membrane-absent systems. Upon closer examination of the simulation trajectories, we found that the key interactions between ligand and proteins remain intact in the membrane-absent systems. For example, as shown in Figure S8, the crucial interactions between ASP97 and GLU288 with the nitrogen atoms of the ligand persist even though the protein and ligand have shifted compared to their initial coordinates. This suggests that the ligands remain bound to the binding site, and the higher ligand RMSD in the chemokine CXCR4 system without a membrane is attributed to the increased RMSD of protein structures. This observation also explains why the performance of ΔΔG predictions remains comparable irrespective of whether the membrane is present or absent in the chemokine CXCR4 system. Although the small molecules remain confined within the binding site due to their strong interactions (e.g., salt bridges) with binding site residues, it is important to acknowledge that the absence of the membrane can lead to significant protein conformational changes, which could potentially result in the movement of the ligand out of the binding site, leading to inaccurate ΔΔG predictions.

We then investigated why the performance of ΔΔG predictions in the adenosine A2A system is better in the membrane-present systems. We identified the influence of lipids as a potential contributor. As shown in Figure S9, we observed that three lipids are within 9 Å of the small molecule, falling within the cutoff for nonbond interactions. The nonbond interactions from the lipid molecules could be a factor contributing to the higher accuracy in ΔΔG predictions in membrane-present conditions.

Conclusions

In this study, we utilized both AMBER-TI and AToM-OpenMM to estimate the ΔΔG values for 53 transformation pairs across four GPCR membrane proteins. Both methods demonstrated comparable accuracy compared with soluble proteins, suggesting promising approaches for binding affinity calculations in membrane protein systems that are crucial for drug discovery. For the tested transformations, 12 λ windows (λ values from 0 to 1) with AMBER-TI and 6 λ windows (λ values from 0 to 1/2) with AToM-OpenMM appear to be sufficient for an accurate ΔΔG prediction. Moreover, a simulation length of 5 ns per window is adequate to obtain reliable ΔΔG values for both approaches.

When comparing AMBER-TI and AToM-OpenMM, AMBER-TI shows slightly better performance. In addition, AMBER-TI simulations are faster than those of AToM-OpenMM. AMBER-TI simulations take approximately 5 hours, whereas AToM-OpenMM simulations require around 45 hours with the same benchmark system: a 60,000-atom system with a single NVIDA A40 GPU simulating 12 λ windows and 5 ns per window (AMBER-TI) and 6 λ windows for each leg and 5 ns per window (AToM-OpenMM), respectively. However, in our simulations, we set the asynchronous replica-exchange replica cycle time to only 4 ps (1000 steps). One can use a larger cycling time (e.g., 20,000 steps) to achieve better performance. For instance, with 20,000 steps, a 5 ns simulation for the same system would only take 22 hours. Another way to enhance efficiency is by utilizing GPUs in combination with CPUs. For example, using one GPU and four CPUs, we completed 5 ns simulations in approximately 16 hours for the same system and GPU type. In addition, AToM-OpenMM can be easily employed for charge-changing transformation pairs as both ligands remain present in the systems throughout the entire simulation period. It is worth noting that a study by Chen et al. highlighted convergence issues for charge-changing cases.50 Therefore, more λ windows and longer simulations may be required for better convergence for these cases.

We also attempted to predict ΔΔG values for the same 53 transformation pairs in membrane-absent systems to assess the performance of ΔΔG prediction without the membrane. Although we achieved relatively good performance, the membrane-present systems show better accuracy in ΔΔG prediction. In our tested cases, all of the ligands bound to the solvent-exposed binding site, which experiences less influence from lipids compared to a lipid-exposed binding site. In 2021, Dickson et al. used AMBER-TI for ΔΔG prediction for the ligands binding to extrahelical sites, which are completely exposed to lipids.51 We hypothesize that the ΔΔG predictions in membrane-absent conditions, particularly for ligands bound to a lipid-exposed binding site, could diverge significantly from those obtained in membrane-present conditions. Moreover, membrane proteins like GPCRs are complex systems with a number of allosteric sites that can be regulated by lipids, modulating ligand binding and cellular signaling.52 Therefore, maintaining the membrane in the system is crucial for obtaining more accurate ΔΔG values.

Furthermore, studies have demonstrated that certain lipids, such as cholesterol, can influence the ligand binding activity. For instance, in 2004, Pucadyil et al. reported that removal of cholesterol from the membrane decreased the ligand binding activity to the 5-HT1A receptor.53 In addition, many experimentally determined membrane protein structures not only feature ligands but also include lipids in their structure files, such as 3D4S (β2 adrenergic receptor),54 4NC3 (5-HT2B receptor),55 and 5C1M (μ-opioid receptor).56 This underscores the significance of the lipids, which has the potential to affect the binding interaction between protein and ligands. Therefore, incorporating diverse lipid types, including cholesterol, to better mimic lipid composition could be helpful in obtaining improved performance in ΔΔG predictions using alchemical free energy calculation methods. Testing various lipid compositions could prove valuable in validating the results in future studies.

Generating correct inputs and establishing systems to calculate ligand binding affinity are time-consuming and error-prone tasks. In 2020, Kim et al. introduced a CHARMM-GUI module called Free Energy Calculator,57 designed to assist researchers in this process, including the setup for membrane proteins. To validate their inputs, they calculated ΔΔG for the ligands in adenosine A2A receptor using FEP/REMD, implemented in NAMD58 and GENESIS.59 CHARMM-GUI Free Energy Calculator provides an easy-to-use interface to help researchers efficiently generate reliable inputs for ΔG and ΔΔG calculations, thereby facilitating advancements in drug discovery and membrane protein research. In this context, supporting AToM-OpenMM in the CHARMM-GUI Free Energy Calculator in the future could facilitate its usage for various pharmaceutically important targets.

Acknowledgments

The authors thank Sunhwan Jo for proofreading and critiques on this manuscript. This work has been supported by NIH GM138472 and NSF MCB-2111728.

Data Availability Statement

The AMBER-TI and AToM-OpenMM topology files, input files, and analysis scripts are available at https://github.com/haz519/MembFE.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.4c00764.

  • The detailed parameters of λ1, λ2, α, and u0 used in AToM-OpenMM (Tables S1 and S2); the detailed MUE, RMSE, MCC, r, and ρ of each GPCR (Tables S3–S6); the transformation pairs used in this study (Figures S1–S4); the RMSD of protein TMDs over the simulations relative to the initial structures for both membrane-present and membrane-absent conditions (Figure S5); the time evolution of RMSD of protein TMDs for four example cases (Figure S6); the ligand RMSD for both membrane-present and membrane-absent conditions (Figure S7); the snapshots of ligand 1t for the initial structures and after 5 ns simulations at λ = 0 window in chemokine CXCR4 system (Figure S8); and the snapshot of the transformation pair from ligand 25f to ligand 25a in the adenosine A2A system and the lipids within 9 Å of ligand 25f (Figure S9) (PDF)

The authors declare the following competing financial interest(s): W.I. is the co-founder and CEO of MolCube INC.

Supplementary Material

ci4c00764_si_001.pdf (2.4MB, pdf)

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ci4c00764_si_001.pdf (2.4MB, pdf)

Data Availability Statement

The AMBER-TI and AToM-OpenMM topology files, input files, and analysis scripts are available at https://github.com/haz519/MembFE.

Articles from Journal of Chemical Information and Modeling are provided here courtesy of American Chemical Society

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